图1.1中的返回分布具有相同的VaR。但是，第二次分布的潜在损失明显比

Figure 1.1 Returns distribution has the same VaR. However, the potential loss of the second distribution obviously much larger than the first loss. When percent (100-X) adverse scenario occurs, the value of the portfolio has a second distribution is expected to suffer a greater loss than the first. Therefore, as a method to solve this problem, the loss of the tail should be used (not consider the tail of the distribution) measurement method, which is called the expected shortfall (Hull, and Basu, 2016). Expected shortfall is the expected loss during the N days, provided that the loss is greater than the VaR estimate (Saunders, 2000). For example, X = 99 and N = 10 case, the deficit is expected to average amount portfolio loss 10 days, 10 days when the loss is greater than 99% VaR time. Therefore, the gap is expected to be used as an effective complement to VaR estimates

The return distribution in Figure 1.1 has the same VaR. However, the potential loss of the second distribution is significantly greater than the loss of the first. When a negative scenario (100-X) occurs, the portfolio value with a second distribution characteristic is expected to suffer a greater loss than the first. Therefore, as a means of solving this problem, a measure of tail loss (not taking into account tail distribution) should be used, which is known as the expected shortage (Hull and Basu, 2016). The expected deficit is the expected loss for the N-day period, provided that the loss is greater than VaR estimates (Saunders, 2000). For example, in the case of X-99 and N-10, the expected deficit is the average amount of the portfolio's loss within 10 days, when the loss is greater than 99% VaR for 10 days. Therefore, the expected gap can be an effective complement to the VaR estimate

The return distribution in Figure 1.1 has the same var. However, the potential loss of the second distribution is significantly greater than that of the first. When (100-x)% adverse scenarios occur, the portfolio value with the second distribution feature is expected to suffer a greater loss than the first one. Therefore, as a way to solve this problem, tail loss (tail distribution cannot be considered) should be measured, which is called expected shortage (hull and Basu, 2016). The expected deficit is the expected loss over the n-day period, provided the loss is greater than the VaR estimate (Saunders, 2000). For example, in the case of x = 99 and N = 10, the expected deficit is the average amount of the portfolio's loss in 10 days, when the loss is greater than 99% VaR in 10 days. Therefore, the expected gap can be an effective supplement to VaR Estimation<br>